On commuting varieties of parabolic subalgebras

Let $G$ be a connected reductive algebraic group over an algebraically closed field $k$, and assume that the characteristic of $k$ is zero or a pretty good prime for $G$. Let $P$ be a parabolic subgroup of $G$ and let $\mathfrak p$ be the Lie algebra of $P$. We consider the commuting variety $\mathcal C(\mathfrak p) = \{(X,Y) \in \mathfrak p \times \mathfrak p \mid [X,Y] = 0\}$. Our main theorem gives a necessary and sufficient condition for irreducibility of $\mathcal C(\mathfrak p)$ in terms of the modality of the adjoint action of $P$ on the nilpotent variety of $\mathfrak p$. As a consequence, for the case $P = B$ a Borel subgroup of $G$, we give a classification of when $\mathcal C(\mathfrak b)$ is irreducible; this builds on a partial classification given by Keeton. Further, in cases where $\mathcal C(\mathfrak p)$ is irreducible, we consider whether $\mathcal C(\mathfrak p)$ is a normal variety. In particular, this leads to a classification of when $\mathcal C(\mathfrak b)$ is normal.Comment: 19 pages; minor update

Desafiar el orden establecido: la necesidad de “localizar” la protección

Existe una crítica cada vez mayor a los actores de protección por ignorar las estrategias de resolución de problemas y las capacidades de los autóctonos, lo que debería impulsar que se reconsideraran radical y creativamente las actitudes y los enfoques

Reflexiones desde el terreno

Trabajar con los líderes religiosos es esencial cuando se proporciona ayuda a las comunidades autóctonas, así como comprender su vida religiosa y cómo las creencias influyen en su toma de decisiones

The Integration of Positron Emission Tomography With Magnetic Resonance Imaging

A number of laboratories and companies are currently exploring the development of integrated imaging systems for magnetic resonance imaging (MRI) and positron emission tomography (PET). Scanners for both preclinical and human research applications are being pursued. In contrast to the widely distributed and now quite mature PET/computed tomography technology, most PET/MRI designs allow for simultaneous rather than sequential acquisition of PET and MRI data. While this offers the possibility of novel imaging strategies, it also creates considerable challenges for acquiring artifact-free images from both modalities. This paper discusses the motivation for developing combined PET/MRI technology, outlines the obstacles in realizing such an integrated instrument, and presents recent progress in the development of both the instrumentation and of novel imaging agents for combined PET/MRI studies. The performance of the first-generation PET/MRI systems is described. Finally, a range of possible biomedical applications for PET/MRI are outlined

‘Smart Cities’ – Dynamic Sustainability Issues and Challenges for ‘Old World’ Economies: A Case from the United Kingdom

The rapid and dynamic rate of urbanization, particularly in emerging world economies, has resulted in a need to find sustainable ways of dealing with the excessive strains and pressures that come to bear on existing infrastructures and relationships. Increasingly during the twenty-first century policy makers have turned to technological solutions to deal with this challenge and the dynamics inherent within it. This move towards the utilization of technology to underpin infrastructure has led to the emergence of the term ‘Smart City’. Smart cities incorporate technology based solutions in their planning development and operation. This paper explores the organizational issues and challenges facing a post-industrial agglomeration in the North West of England as it attempted to become a ‘Smart City’. In particular the paper identifies and discusses the factors that posed significant challenges for the dynamic relationships residents, policymakers and public and private sector organizations and as a result aims to use these micro-level issues to inform the macro-debate and context of wider Smart City discussions. In order to achieve this, the paper develops a range of recommendations that are designed to inform Smart City design, planning and implementation strategies

THOR 2.0: Major Improvements to the Open-Source General Circulation Model

THOR is the first open-source general circulation model (GCM) developed from scratch to study the atmospheres and climates of exoplanets, free from Earth- or Solar System-centric tunings. It solves the general non-hydrostatic Euler equations (instead of the primitive equations) on a sphere using the icosahedral grid. In the current study, we report major upgrades to THOR, building upon the work of Mendon\c{c}a et al. (2016). First, while the Horizontally Explicit Vertically Implicit (HEVI) integration scheme is the same as that described in Mendon\c{c}a et al. (2016), we provide a clearer description of the scheme and improved its implementation in the code. The differences in implementation between the hydrostatic shallow (HSS), quasi-hydrostatic deep (QHD) and non-hydrostatic deep (NHD) treatments are fully detailed. Second, standard physics modules are added: two-stream, double-gray radiative transfer and dry convective adjustment. Third, THOR is tested on additional benchmarks: tidally-locked Earth, deep hot Jupiter, acoustic wave, and gravity wave. Fourth, we report that differences between the hydrostatic and non-hydrostatic simulations are negligible in the Earth case, but pronounced in the hot Jupiter case. Finally, the effects of the so-called "sponge layer", a form of drag implemented in most GCMs to provide numerical stability, are examined. Overall, these upgrades have improved the flexibility, user-friendliness, and stability of THOR.Comment: 57 pages, 31 figures, revised, accepted for publication in ApJ

Simultaneous in vivo positron emission tomography and magnetic resonance imaging

Positron emission tomography (PET) and magnetic resonance imaging (MRI) are widely used in vivo imaging technologies with both clinical and biomedical research applications. The strengths of MRI include high-resolution, high-contrast morphologic imaging of soft tissues; the ability to image physiologic parameters such as diffusion and changes in oxygenation level resulting from neuronal stimulation; and the measurement of metabolites using chemical shift imaging. PET images the distribution of biologically targeted radiotracers with high sensitivity, but images generally lack anatomic context and are of lower spatial resolution. Integration of these technologies permits the acquisition of temporally correlated data showing the distribution of PET radiotracers and MRI contrast agents or MR-detectable metabolites, with registration to the underlying anatomy. An MRI-compatible PET scanner has been built for biomedical research applications that allows data from both modalities to be acquired simultaneously. Experiments demonstrate no effect of the MRI system on the spatial resolution of the PET system and <10% reduction in the fraction of radioactive decay events detected by the PET scanner inside the MRI. The signal-to-noise ratio and uniformity of the MR images, with the exception of one particular pulse sequence, were little affected by the presence of the PET scanner. In vivo simultaneous PET and MRI studies were performed in mice. Proof-of-principle in vivo MR spectroscopy and functional MRI experiments were also demonstrated with the combined scanner